Master Thesis

P-release kinetic as a predictor for P-availability in the STYCS Trials

Marc Jerónimo Pérez y Ropero

Introduction

  • In my Internship I studied the current GRUD, particularly Mg, P and K

  • Fertilizer requirement models imply \(Y\sim STP + Clay\) & \(P-\text{Export}\sim STP + Clay\)

  • Currently only stationary measurement of STP are considered

  • Could a kinetic desorption-model better explain the soil status and yield data?

The STYCS Experiment

  • LTE STYCS, all treatment conditions equal except P-fertilization, which is in 6 Levels, 3 were considered(\(P0\),\(P100\),\(P166\))
  • 4 Sites regarded; Ellighausen, Rümlang-Altwi, Oensingen, Zürich-Reckenholz
  • 5 Sites, 4 blocks per site, 6 Treatment-Levels, 4 Repetitions
  • Years 2017-2022 were modelled, kinetic data was collected only for year 2022

A kinetic Approach to P

The net-desorption was modeled using a first-order kinetic equation:

1. The Rate of Release: The change in P over time is proportional to the remaining desorbable P. \[\frac{dP}{dt}=k \times (P^S-P)\]

2. The Solution: When solved, this gives us the equation for the curve: \[P(t)=P^S \times (1-e^{-kt})\]

  • \(P^S\) (PS): The maximum desorbable P pool.
  • \(k\): The first-order rate constant.

Adapted Kinetic-Experiment Setup

Method Validation

Method Validation

Method Validation

Method Validation

The Competing Predictors

We compared two approaches to predict agronomic outcomes:

The Standard Method

  • \(P_{CO2}\)
  • \(P_{AAE10}\)

These are static “snapshots” of the soil’s P capacity.

The Kinetic Method

  • PS (\(P^S\)): The size of the available P pool.
  • k: The rate of P release.

This approach measures P as a dynamic process.

Measuring Success: The Key Outcomes

We tested the models against three agronomic metrics:

1. Normalized Yield (\(Y_{norm}\)) - How well did the crop perform relative to its maximum potential at that specific site?

2. P-Export (\(P_{up}\)) - How much phosphorus did the crop remove from the field?

3. P-Balance (\(P_{bal}\)) - What is the long-term surplus or deficit of P in the soil? This is a key indicator of sustainability.

How We Compared the Models

To ensure a fair and robust comparison, we used a consistent statistical approach:

1. Linear Mixed-Effects Models (lmer) - We built a separate model for each agronomic outcome (Yield, P-Export, P-Balance). - This approach accounts for the nested structure of the STYCS experiment (sites, years, blocks).

2. Standardized Coefficients (β) - All numeric variables were scaled and centered (mean=0, sd=1). - This allows us to directly compare the effect size of each predictor. A larger coefficient means a stronger effect.

3. The Comparison - In the following tables, each column represents a separate model where we test a different set of predictors.

What Do the P Metrics Actually Measure?

A robust P metric should reflect both the soil’s inherent properties (like texture and pH) and the impact of management (fertilization). We modeled each metric to see what drives it.

Model $PS$ $k$ $J_0$ $P_{CO_2}$ $P_{AAE10}$
Alox 0.136 -0.660 -1.204 -0.034 -0.319
Feox -0.098 0.020 -0.571 -0.164 -0.138
Clay -0.062 -1.733** 0.611 -0.007 -0.121
$C_{org}$ 0.351* 1.044** -0.412 0.166 0.232
pH -0.058 -0.280 0.094 0.075 0.057
Silt -0.046 0.252 0.113 -0.084 0.012
$R^2_m$ 0.175 0.204 0.224 0.125 0.280
$R^2_c$ 0.894 0.963 0.976 0.724 0.832

QII & III: STP, k & PS correlate to soil properties?

The following random structure was chosen:

(1|year) + (1|Site) + (1|Site:block) + (Treatment|Site)

Do P-CO2, P_AAE10, k and PS correlate with soil characteristics?

Coefficient Table for Soil Covariates. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Model m.PS m.k m.log(k*PS) m.PCO2 m.PAAE10
(Intercept) -0.848* -0.425 0.039 -0.536 -0.532
Alox 0.136 -0.660 -1.204 -0.034 -0.319
Feox -0.098 0.020 -0.571 -0.164 -0.138
soil_0_20_clay -0.062 -1.733** 0.611 -0.007 -0.121
soil_0_20_Corg 0.351* 1.044** -0.412 0.166 0.232
soil_0_20_pH_H2O -0.058 -0.280 0.094 0.075 0.057
soil_0_20_silt -0.046 0.252 0.113 -0.084 0.012
R2m 0.175 0.204 0.224 0.125 0.280
R2c 0.894 0.963 0.976 0.724 0.832

Observation

  • P-CO2 and P-AAE10 did not correlate with clay-content
  • k does not correlate with Treatment but with pH and silt-content
  • \(k*log(PS)\) had significant effects for clay- and silt-content as well as pH, but lower in Treatment
  • PS was the covariate best predicted by soil properties: \(R^2_m=0.858\)

QIV & V: Correlation k, PS & STP to Yield and P-metrics

Yield model summary:

Coefficient Table for Yield Variables. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Model Yn-STP-CO2 Yn-STP-AAE10 Yn-STP-GRUD Yn-Kinetic
(Intercept) 0.012 0.007 -0.109 0.156
k 0.166
k:log(PS) -0.012
log(PS) 0.066
log(soil_0_20_P_AAE10) 0.067* 0.432**
log(soil_0_20_P_CO2) 0.027 -0.128
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) 0.149*
R2m 0.012 0.084 0.291 0.019
R2c 0.083 0.361 0.436 0.045

Observation

  • \(k*log(PS)\) and \(k\) showed the strongest effects in the prediction of Ynorm and Yrel
  • P-AAE10 did show a significant effect in prediction of Yrel

P-Export model summary:

Coefficient Table for P-export. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Model CO2_Pexport AAE10_Pexport Grud_Pexport Kin_Pexport
(Intercept) 0.012 -0.002 0.119 0.596
k -0.014
k:log(PS) 0.080
log(PS) -0.018
log(soil_0_20_P_AAE10) 0.025 -0.015
log(soil_0_20_P_CO2) 0.087 0.131
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) 0.011
R2m 0.012 0.001 0.016 0.004
R2c 0.654 0.685 0.796 0.789

Observations

  • P-CO2 did show strong effects in predicting Pexport

P-balance model summary:

Coefficient Table for P-balance. Significant codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
Model CO2_Pbalance AAE10_Pbalance Grud_Pbalance Kin_Pbalance
(Intercept) 0.569* 0.315 0.610* 1.086*
k 0.155
k:log(PS) -0.151
log(PS) 0.341***
log(soil_0_20_P_AAE10) 0.009 0.009
log(soil_0_20_P_CO2) -0.023 -0.029
log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) 0.030
R2m 0.001 0.000 0.006 0.122
R2c 0.590 0.762 0.596 0.699

Observation

  • \(PS\) showed the strongest effect in predicting P_balance and k showed substantial \(R^2_m\)

Concluding Remarcs

  • The net-desorption of P probably follows a first-order-kinetic, but \(PS\) is difficult to directly estimate.
  • The kinetic parameters \(k\) and \(PS\) could comparably and sometimes better explain Ynorm, Yrel and P-Balance.
  • Regarding the difference between \(R^2_m\) and \(R^2_C\) confounded effects seem to be buried in the sites.
  • P-CO2 and P-AAE10 are not as well explainable as \(PS\) and \(k\), in particular not by clay-content.
  • P-CO2 correlated however significantly with P-Export

Thank you for your attention